Conservation laws for a modified lubrication equation. (December 2015)

• Record Type: Journal Article
• Authors: Wei, Long
• Is Part Of: Nonlinear analysis. Volume 26(2015)
• Page Start: 44
• Page End: 55
• Publication Date: 2015-12
• Subjects: Nonlinear self-adjointness -- Lagrangian with an auxiliary function -- Conservation law; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.04.005
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this work we study the conservation laws of a modified lubrication equation, which describes the dynamics of the interfacial motion in phase transition. We show that the equation is nonlinear self-adjoint and has an exact Lagrangian with an auxiliary function. As a result, by a general theorem on conservation laws proved by Nail Ibragimov recently and Noether's theorem, some new conservation laws for the equation are obtained. Our results show that the non-locally defined conservation laws generated by Noether's theorem are equivalent to the local ones given by Ibragimov's theorem.